Proth Search Page |

Rebuilt and maintained by Wilfrid Keller

Primes k · 2 + 1 ^{n} |
List of primes for k < 300
List of primes for 300 < k < 600
List of primes for 600 < k < 900
List of primes for 900 < k < 1200
Frequencies (extended and corrected) History |

Fermat numbers |
Standard factoring status
Factors of generalized Fermat numbers GFN03 factoring status GFN05 factoring status GFN06 factoring status GFN07 factoring status GFN10 factoring status GFN11 factoring status GFN12 factoring status Search limits and reservations |

Primes k · 2 − 1 ^{n} |
List of primes for k < 300 |

The Sierpiński problem |
Definition and status |

The Riesel problem |
Definition and status |

Cullen primes |
Definition and status
Generalized Cullen primes (new) |

Woodall primes |
Definition and status |

Lists of primes

all currently known primes included.

GFNfacs.html now contains

128 of which were found during this year.

2023 had again been a productive year for GFN factors:

470 divisibilities found!

Number of divisibilities discovered in previous years:

362 (2022), 747 (2021), 624 (2020), 41 (2019), 27 (2018),

18 (2017), 46 (2016), 79 (2015), 136 (2014), 213 (2013),

457 (2012).

November 27, 2023:

Frequencies table corrected for 1200 <

adjusted count for 80000 <

Four

month of 2023:

June 25, 2023:

New factor of Fermat number F(425).

May 31, 2023:

New factor of Fermat number F(1784).

April 23, 2023:

April 21, 2023:

New factor of Fermat number F(1436).

April 16, 2023:

Frequencies table corrected for 1200 <

counts for 100000 <

February 9, 2023:

New factor of Fermat number F(1493).

December 2022:

November 27, 2022:

July 25, 2022:

number found:

March 8, 2022:

A second long-term omission was detected in the list

of primes

to be added.

November 25, 2021:

November 24, 2021:

New factor of Fermat number F(1379).

August 11, 2021:

New factor of Fermat number F(66643).

June 29, 2021:

First factor of GF(9,11) found, a P52 prime.

May 2021:

A long-term omission was detected in the list of primes

than six months:

March 27, 2021:

6896-digit final factor of xGF(13,7,5) proven prime.

March 12, 2021:

First factor of GF(14,10) found, a P37 prime.

March 1st, 2021:

New factor of Fermat number F(40).

December 31, 2020:

In 2020, 612 GFN divisibilities were found:

501 by Gary Gostin, 111 by others.

October 05, 2020:

found:

The same prime also divides GF(18233952,7), the largest

known composite GF(

July 06, 2020:

Summary of frequencies corrected and extended.

April 01, 2020:

found:

GF(13334486,7) and others.

February 11, 2020:

Gary Gostin starts generating new GFN divisibilities:

82 factors delivered at once.

February 10, 2020:

New factorization at GFNsmall.html:

Cofactor of 10^(2^8) + 3^(2^8) is P85 × P105.

January 22, 2020:

New factor of Fermat number F(5523858):

December 25, 2019:

December 9, 2019:

New factor of Fermat number F(2587), which brings to 350

the total number of known factors.

October 16, 2019:

New factors of Generalized Fermat numbers GF(4800313,3)

and GF(4800310,5).

October 14, 2019:

New factor of Generalized Fermat number GF(4673541,7).

October 13, 2019:

New factor of Generalized Fermat number GF(4532462,11).

September 29, 2019:

New factor of Generalized Fermat number GF(3964696,11).

July 31, 2019:

Generalized Fermat number GF(25,10) proved composite.

July 6, 2019:

Generalized Fermat number GF(24,10) proved composite.

March 23, 2019:

New factor of Fermat number F(9863).

January 28, 2019:

New factor of Fermat number F(118).

December 31, 2018:

Table of factors GFNfacs.html now includes 6608

new divisibilities, 21 of them found in 2018.

December 19, 2018:

New factor of Fermat number F(132).

December 13, 2018:

New factor of Fermat number F(3345).

November 2, 2018:

New factor of Fermat number F(2144).

July 24, 2018:

New factor of Fermat number F(5199), which brings to 300

the total number of known composite Fermat numbers.

May 1, 2018:

New factor of Generalized Fermat number GF(10746,12).

April 5, 2018:

New factor of Fermat number F(274).

April 3, 2018:

Candidate of Extended Sierpinski Problem eliminated.

March 10, 2018:

New factor of Fermat number F(63480).

January 15, 2018:

New factorization at GFNsmall.html:

Cofactor of 11^(2^8) + 10^(2^8) is P62 × P107 .